Scientists applied an unusual mathematical approach in the equations of spacetime curvature and obtained a new type of charged black hole. Their behavior turned out to be surprisingly familiar: this is how Water in a pot behaves when it starts to boil. At a certain combination of pressure, volume, and temperature, the difference between a "liquid" and "gaseous" black hole vanishes. This is exactly like the critical point of water: steam and liquid become indistinguishable.
Even Stephen Hawking and Jacob Bekenstein proved that black holes have temperature and entropy (a measure of disorder). The new research adds that the transitions between states of these objects obey the same laws as steam boiling. Most unexpectedly: if you remove the mathematical "seasoning" from the calculations, the black hole behaves exactly like an ideal gas describing the transformation of water into steam.
as written by the authors arXiv:2512.19200
In this work, we derive a new class of charged black holes by introducing Dunkl derivatives in the four dimensional spacetime. To construct such solutions, we first compute the Ricci tensor and the Ricci scalar using the Christoffel symbols. Substituting them into the modified Einstein field equations via extended Dunkl derivations, we obtain the metric function of charged Dunkl black holes. Next, we investigate the charge effect on the corresponding thermodynamical properties by computing the associated quantities. To study the thermal stability, we calculate the heat capacity. After that, we approach the P-v criticality behaviors by determining the critical pressure Pc, the critical temperature Tc and the critical specific volume vc in terms of Q and two parameters A and B carrying data on the Dunkl reflections. Precisely, we show that the ratio Pcvc Tc is a universal number with respect to the charge Q and B parameters. Taking a zero limit of A, we recover the Van der Waals fluid behaviors. For Joule-Thomson expansion effects for such charged black holes, we reveal certain similarities and the differences with Van der Waals fluids. Finally, we discuss the phase transitions via the Gibbs free energy computations.
Black holes are not eternal: due to Hawking radiation, they slowly evaporate. A tiny black hole could "boil" away and vanish in a fraction of a second.